Bridger Holden

2022-09-06

properties of logarithms $\mathrm{ln}12-\mathrm{ln}2=\mathrm{ln}6$
I checked wolframalpha and it says that ln12-ln2=ln6. How? i tried to do: ln12=ln(2*2*3) which may be 2ln(2*3) (which is probably wrong). I need help.
EDIT: Ok, thanks. Actually i could have just searched logarithms properties on google(didn't think about it). Sorry for taking your time.

Krha77

You need to remember that
$\mathrm{ln}a-\mathrm{ln}b=\mathrm{ln}\left(\frac{a}{b}\right)$
Applying that here gives you
$\mathrm{ln}\left(12\right)-\mathrm{ln}\left(2\right)=\mathrm{ln}\left(\frac{12}{2}\right)=\mathrm{ln}\left(6\right)$
Note, alternatively, that we can use the property
$\mathrm{ln}\left(ab\right)=\mathrm{ln}a+\mathrm{ln}b$
as well.
$\mathrm{ln}\left(12\right)=\mathrm{ln}\left(2\cdot 6\right)=\mathrm{ln}\left(2\right)+\mathrm{ln}6$
So
$\mathrm{ln}\left(12\right)-\mathrm{ln}2=\mathrm{ln}2+\mathrm{ln}6-\mathrm{ln}2=\mathrm{ln}6$

Sonia Rowland

Hint: Use the property
$\mathrm{ln}x-\mathrm{ln}y=\mathrm{ln}\frac{x}{y}.$

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